So, just to clarify, because I'm still fuzzy on the terms for perspectives in older games myself, examples of an oblique perspective can be seen in many older RPGs (Earthbound, Final Fantasy, Secret Of Mana, etc.).

I've seen many games created in this perspective that utilize a more action-oriented style of gameplay in which one can see various physical interactions at work, such as projectiles, jumping, friction, and more. (Alundra is one that always stands out in my mind)

My question is: How are the physics often being done from a design/engine perspective in these games? Are there common practices for this sort of game design?

2 Answers
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The presentation consists of several layers of content, for instance, Secret of Mana on the SNES uses (from memory):

Far backdrop(used for parallax)

backdrop

active scenery

characters/sprites

foreground

UI

You can examine this for yourself using a SNES emulator such as ZSNES, and disabling various layers.

As to how physics are done, just consider each layer as a discrete 2d vertical plane.
For collision detection, each object would have a hit box, and collision detection would go Bounding Circle -> Axis Aligned Bounding Rectangle -> Per Pixel (modern systems can use frame buffers on the GPU to improve the efficiency of this, by rendering each object as a mask of different colours).

If by physics, you mean collision detection and such, I would recommend that you visualize the world from the top view while rendering it in the oblique view. For example, if you have a box, give it properties like GroundWidth, GroundBreadth, GroundPosition, etc. along with your other properties like TextureWidth and TextureHeight.